Suppose a differntiable function f(x) satisfies the identity f(x+y)=f(x)+f(y)+xy2+x2y±,for all real x and y. If limx→0f(x)x=1, then f'(3) is equal to ___________ .

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answer is 10.

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Detailed Solution

From first principle of differentiationf'x=limh→0fx+h−fxh==limh→0fx+fh+xh2+x2h−fxh=limh→0fhh+x2=1+x2Therefore,f'3=32+1=10

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